Spatial position determination system

ABSTRACT

A system is disclosed that determines a spatial position of a tracker device relative to an object sending a return signal to the tracker. Such a system advantageously maintains phase accuracy between a forward signal from the tracker device and the return signal from the object. The system can include, as part of a tracker device, a reference signal generator, a transmitter, a receiver, and a spatial position computer. The reference signal generator is responsive to and phase-stabilized by a broadcast signal, e.g., a signal received from a commercial AM broadcast transmitter. The transmitter and receiver are both coupled to and phase-stabilized by the tracker reference signal generator. Variations and methods with different advantageous features are also described.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.09/915,662 filed on Jul. 25, 2001, now U.S. Pat. No. 6,867,693.

BACKGROUND OF THE INVENTION

The problem of determining the spatial position of objects is an ancientone. Perhaps the simplest and oldest known solution is to pace off adistance to a visible object by walking toward it along a straight path.More accurate and recent techniques include triangulating the locationof a hidden object based on estimated distances or azimuthal angles tothe object.

Measurement of azimuthal angle to a given object tends to be lessaccurate than measurement of distance to that object. Extremely preciseinstruments have been developed for distance measurement. For example,an optical instrument disclosed in U.S. Pat. No. 5,430,537 to Liessneret al. purports to have accuracy around the 1–10 micron resolution oflight wavelengths. This instrument is based on phase changes between alight beam sent to a passive reflector and another light beam returnedfrom the reflector.

Less precise instruments for phase-based distance measurement canprovide benefits in particular applications. For example, R. S. Trenam,“Automatic Animal Tracking on a Limited Budget,” in The Collection andProcessing of Field Data (1967) (pp. 273–82), discloses tracking ofsheep to 20-yard accuracy using RF phase measurements.

In any system relying on phase differences between forward and returnsignals, frequency stability of the signals is critical to maintainingaccuracy of distance measurement. Slight frequency deviations in theforward and return signals can cause significant phase deviations,especially when the distance to be measured includes a large number ofwavelengths. Such phase deviations interfere with those expected fromchanges in distance and can significantly degrade accuracy.

SUMMARY OF THE INVENTION

A spatial position determination system according to various aspects ofthe present invention determines a spatial position of a tracker devicerelative to an object sending a return signal to the tracker. Such asystem advantageously maintains phase accuracy between a forward signalfrom the tracker device and the return signal from the object.

A system according to particularly advantageous aspects of the inventionincludes, as part of a tracker device, a reference signal generator, atransmitter, a receiver, and a spatial position computer. The referencesignal generator is responsive to and phase-stabilized by a broadcastedsignal, e.g., a signal received from a commercial AM broadcasttransmitter. The transmitter and receiver are both coupled to andphase-stabilized by the tracker reference signal generator. The spatialposition computer is coupled to the receiver and (1) the trackerreference signal generator or (2) the tracker transmitter, or (3) both.The spatial position computer is responsive to indicia of a phaserelationship between an output signal from the tracker transmitter andan input signal to the tracker receiver. Based on that indicia, thespatial position computer determines the spatial position of the trackerrelative to the input signal source.

A spatial position can be expressed in a number of ways. It can beexpressed as a stationary position, i.e., a point in space.Alternatively, it can be expressed as a differential position, e.g., avelocity or an offset from a previous spatial position. In addition, aspatial position can be expressed as a physical measure of distance, oras a proportion of a wavelength of the input signal.

A spatial position determination system according to particular aspectsof the invention advantageously includes a transponder coupled via fieldradiation to the tracker and triggered by it to produce a return signal.The transponder includes a transmitter and a receiver, which are coupledvia field radiation to the tracker receiver and transmitter,respectively. A tracker's spatial position computer in such a system isresponsive to indicia of a phase relationship between an output signalfrom the tracker transmitter and an input signal received from thetransponder transmitter. Based on that indicia, the spatial positioncomputer determines the spatial position of the tracker relative to thetransponder.

A transponder in a system according to further aspects of the inventionincludes its own reference signal generator, which is responsive to andphase-stabilized by a broadcasted signal. The receiver and transmitterin such a transponder are coupled to and phase-stabilized by thetransponder reference signal generator. In such a system, the trackerreference signal generator and the transponder reference signalgenerator can both be responsive to the same broadcasted signal.

Phase-stabilized and phase-stabilizing signal generators according tofurther aspects of the invention include a stabilizing DDS (directdigital synthesis) module having a phase accumulator that is clockedresponsive to sync pulses, and an output DDS module. The output DDSmodule is coupled to the stabilizing DDS module and has a phaseaccumulator that is clocked by system clock pulses but forced to theaccumulated phase of the first DDS module upon occurrence of a qualifiedsync pulse.

The above summary does not include an exhaustive list of all aspects ofthe present invention. Indeed, the inventor contemplates that hisinvention includes all systems and methods that can be practiced fromall suitable combinations of the various aspects summarized above, aswell as those disclosed in the detailed description below andparticularly pointed out in the claims filed with the application. Suchcombinations have particular advantages not specifically recited in theabove summary.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the present invention are described below withreference to the drawings, wherein like designations denote likeelements.

FIG. 1 is a simplified perspective view of a tracker device and atransponder device in a phase-referencing pet location system accordingto various aspects of the invention.

FIG. 2 is a schematic block diagram of the tracker and transponderdevices of FIG. 1.

FIG. 3 is a schematic block diagram of a signal processing system thatcan be employed in the tracker and transponder devices of FIG. 2.

FIG. 4 is a schematic block diagram of a reference signal generator inthe signal processing system of FIG. 3.

FIG. 5 is a schematic block diagram of a transmitter in the signalprocessing system of FIG. 3.

FIG. 6 is a schematic block diagram of a receiver in the signalprocessing system of FIG. 3.

FIG. 7 is a functional flow diagram of a spatial position determinationprocess according to various aspects of the invention.

FIG. 8 is a data flow diagram of a method for determining changes inspatial position according to various aspects of the invention.

FIG. 9 is a data flow diagram of a method for determining spatialposition expressed as an azimuthal angle according to various aspects ofthe invention.

FIG. 10 illustrates multiple signals produced during a simulation ofphase stabilization according to various aspects of the presentinvention with a fairly accurate system clock frequency.

FIG. 11 illustrates multiple signals produced during a simulation ofphase stabilization with a less accurate system clock frequency.

FIG. 12 illustrates a simulated bandpass-filtered output signal from anunstabilized DDS (direct digital synthesis) module using a system clockfrequency that degrades in accuracy with time.

FIG. 13 illustrates a simulated bandpass-filtered output signal from aDDS module that is phase-stabilized in accordance with various aspectsof the invention, using a system clock frequency that degrades inaccuracy with time.

FIG. 14 is an X-Y plot of the unstabilized output signal of FIG. 12 witha first group of the signal's samples plotted on the X-axis and asecond, later, group of the signal's samples plotted on the Y-axis.

FIG. 15 is an X-Y plot of the stabilized output signal of FIG. 13 with afirst group of the signal's samples plotted on the X-axis and a second,later, group of the signal's samples plotted on the Y-axis.

DESCRIPTION OF PREFERRED EXEMPLARY EMBODIMENTS

A spatial position determination system according to various aspects ofthe present invention provides numerous benefits, including permittinghighly accurate phase-based determination of distance without the needto include a high-stability internal oscillator. An example of such asystem 100 including a tracker device 110 and a transponder 150 attachedto a hidden object (here, a lost dog 155) may be better understood withreference to FIGS. 1–2.

In operation of exemplary system 100, a person holding tracker 110 candetermine the spatial position of tracker 110 relative to transponder150 and, based on repeated updates to that position determination,locate dog 155. By maintaining phase stability responsive to abroadcasted signal from broadcast transmitter 105, both tracker 110 andtransponder 150 cooperate to permit highly accurate (e.g., about 4% of awavelength) distance determination while omitting the expense and bulkof high-stability oscillators.

FIG. 2 schematically depicts functional modules that tracker 110 andtransponder 150 implement. These functional modules can be suitablyimplemented by hardware, software, or both. Functional modules caninteract via any suitable routes of interconnection, including hardware(e.g., a bus, dedicated signal lines, etc.), access to shared storagemedia (e.g., arguments and returned values of function calls in RAMmedia, dual-access RAM, files residing on hard disk media, etc.), andcombinations of hardware and shared media access.

Tracker 110 implements functional modules including: a reference signalgenerator 112; a transmitter 114 and a receiver 116, both coupled togenerator 112; a spatial position computer 118 coupled to receiver 116and generator 112; and an I/O module 120 coupled to computer 118 and toa suitable user interface not shown in FIG. 2. Tracker 110 can alsoinclude a GPS (Global Positioning System) module 122, which canadvantageously cooperate with spatial position computer 118 as discussedbelow.

Transponder 150 implements functional modules including: a referencesignal generator 152; a receiver 154; and a transmitter 156. Receiver154 and transmitter 156 are both coupled to generator 152. They are alsocoupled to each other such that output of receiver 154 controlstransmitter 156.

Tracker 110 and transponder 150 include some of the same types offunctional modules. Both devices include reference signal generators,transmitters, and receivers. These functional modules can be implementedby similar or identical hardware in both devices, with differentsoftware for causing them to operate appropriately for tracker 110 ortransponder 150. For example, transmitter 114 and receiver 116 intracker 110 do not couple to each other. Thus, software in tracker 110need not cause transmitter 114 to control receiver 116.

A reference signal generator according to various aspects of theinvention includes any hardware or software, or combination of both,that is phase-stabilized by a broadcasted signal. With its consequentphase stability, such a generator can phase-stabilize other functionalmodules. A functional module or device is phase-stabilized by abroadcasted signal when the phase stability of its internal operationsand output signal(s) is not substantially worse than if controlled by aninternal clock having phase stability as good as that of the broadcastedsignal. In other words, the output of a device phase-stabilized by abroadcasted signal has phase stability nearly as good as that of thebroadcasted signal itself. If a broadcasted signal's phase stabilitywere such that it has phase noise of only −100 dBc at +/−100 Hz, forexample, an output signal from a device phase-stabilized by the signalwould not be expected to have phase noise of −50 dBc at +/−100 Hz, evenif that were the phase stability of the device's internal oscillator. Asanother example, if the broadcasted signal's phase stability were suchthat the signal's frequency always remained within 0.01 ppm of average,the phase-stabilized device would not be expected to produce an outputsignal deviating 10 ppm from average.

Reference signal generators 112 and 152 of devices 110 and 150 are bothphase-stabilized by a broadcasted signal from broadcast transmitter 105.In the example of FIGS. 1 and 2, transmitter 105 is a commercial AMbroadcast transmitter operating at a frequency between about 500 kHz andabout 1600 kHz. Such transmitters have operating ranges of at leastseveral miles, and their signal quality tends to degrade graduallyrather than abruptly. Consequently, dog 155 of FIG. 1 (with transponder150) and tracker device 110 (typically carried by the dog's owner) areboth likely to be within the coverage zone of transmitter 105.

In a particularly advantageous configuration according to variousaspects of the invention, a reference signal generator phase-stabilizesother functional modules to a degree of stability greater than thegenerator's system clock granularity would conventionally permit. Forexample, conventionally performing a phase adjustment to a directdigital synthesis (DDS) module by skipping or effectively doubling acycle of a 24 MHz system clock (one of many possible frequencies)induces a phase granularity of 1/24 MHz, or 42 nanoseconds. This equatesto 203 degrees of a 13.56 MHz transmit/receive frequency cycle (again,one of many possibilities), which is clearly unacceptable for aphase-based distance measurement system.

Advantageously, a reference signal generator according to variousaspects of the invention can achieve its high level of performancewithout the need for analog phase locking. As discussed below withrespect to a specific embodiment and with reference to FIGS. 4–6 and10–15, this phase stabilization is performed using a combination of syncpulses and qualified sync pulses.

A transmitter according to various aspects of the invention includes anyhardware, software, or combination of both capable of transmitting anoutput signal as field radiation, via a suitable coupling device. Anysuitable type of radiation in any suitable field can be employed,including sound waves below, within, or above the range of human hearingin air or water, and electromagnetic radiation in the RF, infrared, orvisible light spectrum. Suitable coupling devices include antennas(e.g., loops, whips, directional arrays, etc.) for coupling to an RFfield and piezoelectric transducers for coupling to an acoustic field.

The many different types of transmitters suitable for variousembodiments of the invention operate with widely varying output levelsand signal frequencies. For example, an acoustic transmitter for use inthe ocean (e.g., to track movements of marine mammals) may have arelatively high output level and a particular frequency selected foraccuracy, range, avoiding interference with other tracking systems, andminimal adverse impact to the mammal. An optical transmitter aimed fromthe earth to its moon may operate at a very high output power toovercome the significant path loss between the two distant bodies.

Government regulations may severely restrict the output levels andsignal frequencies that RF transmitters can employ in determiningpositions of terrestrial objects. In a preferred implementation ofexemplary system 100 (FIG. 2), transmitters 114 and 156 advantageouslyoperate with an output level of less than one microwatt, at a frequencyof 13.56 MHz, with the only modulation being periodic four-second burstsof a carrier wave. Harmonics are attenuated by 30 dB. This operatingarrangement complies with regulations promulgated by the FederalCommunications Conunission, Part 15 (Section 15.209) for unlicensedtransmitter operation. T. Warnagiris, “Legal Unlicensed Transmitting,”in Applied Microwave & Wireless, Spring 1996, pp. 32–54, which isincorporated herein by reference, provides guidance for implementationof other unlicensed embodiments.

In the preferred implementation of system 100, calculated field strengthat 30 meters from transmitters 114 and 156 is 140 microvolts per meter.Even at this very low power level, system 100 can achieve high accuracy,for example detecting three-foot (4% at 13.56 MHz) distance changes at500 feet of separation and distance changes of about 1.5 foot (2%) at 50feet of separation. Longer integration times than the four secondsemployed in exemplary system 100 can yield even better accuracy or rangeat this low transmit power level.

A variation employing licensed transmitters can operate withsignificantly higher power levels for greater range and reliability. Insuch a variation or others, the transmit and receive frequencies oftracker 110 can be randomly assigned within a narrow band to reduce theprobability of interference with other systems operating in thevicinity. In a variation employing direct sequence spread spectrumtransmission (DSSS), pseudo random sequence codes can be randomlyassigned to likewise avoid interference. Depending on local regulations,it may be possible to employ higher transmit power levels in anunlicensed DSSS variation because the spread spectrum transmissioninterference in a given narrow frequency range is lower than narrowbandtransmission interference within such a range.

A receiver according to various aspects of the invention includes anyhardware, software, or combination of both capable of receiving an inputsignal coupled to it via field radiation and a coupling device of anysuitable type, e.g., whip antenna 112 of FIG. 1. As with a transmitter,any suitable type of radiation in any suitable field can be employed.Preferably, a transmitter and receiver employ the same coupling device.The transmitter and receiver can be suitably isolated from each other byconventional hardware such as a high-Q resonant device (in variationswhere the transmitter and receiver operate at different frequencies),unidirectional (e.g., ferromagnetic) circuitry, or a single-poledouble-throw switch.

By coupling tracker 110 and transponder 150 together via RFelectromagnetic field radiation, system 100 permits determination of aspatial position of tracker 110 relative to transponder 150. Thisspatial position can be expressed as a physical measure of distance,depicted with arrow “d” in FIG. 2. In advantageous variations, thespatial position can be expressed as an offset from a previous spatialposition or as an azimuthal angle from tracker 110 to transponder 150.For example, a particular spatial position may be expressed as anazimuthal angle of 90 degrees, in which case transponder 150 is directlyeast of tracker 110.

Transmitter 114 in tracker 110 transmits a forward signal 15 to receiver154 in transponder 150. Transmitter 156 in transponder 150 replies witha return signal 51, which is received by receiver 116 in tracker 110.Both reference signal generator 152 and receiver 154 couple to andcontrol the output phase of transmitter 156. In exemplary transponder150, receiver 154 sets the output phase of transmitter 156 to the phaseit receives of forward signal 15. (Of course, all such phases arerelative to respective phase offsets induced by intervening signalprocessing.) Thus, changes in phase of return signal 51 aresubstantially determined by changes in distance “d,” which successivemeasurements can detect. A given change in distance “d” results in aphase change in return signal 51 (when received at receiver 116) that isproportional to twice the change in distance.

Receiver 154 and transmitter 156 are both phase-stabilized by referencesignal generator 152. Thus, additional phase instability of returnsignal 51 over that of forward signal 15 substantially corresponds tophase instability of the broadcasted signal from transmitter 105.

An exemplary device 300 that implements a reference signal generator 400and a transmitter 500 and receiver 600, phase-stabilized by generator400 to a broadcasted signal 332 according to various aspects of theinvention, may be better understood with reference to FIG. 3. Operationof device 300 and its generator 400, transmitter 500, receiver 600, andother components are discussed in the context of an advantageousembodiment that illustrates benefits of various aspects of the inventionwhen such aspects are employed. However, certain aspects can providebenefits even when various other aspects are omitted. In addition,device 300 need not be employed as tracker 110 or transponder 150 ofsystem 100 (FIGS. 1–2), though such is presently preferred. Thus,neither this nor any other example provided herein should be consideredas limiting the scope of the invention in any way; that limitingfunction is reserved exclusively for the issued claims.

Device 300 includes various analog and digital components mounted on aprinted circuit board. These components are conventionally arranged andare omitted from FIG. 3 for clarity. Digital components include: amicrocontroller (e.g., a PIC16C73); an FPGA (e.g., a XILINX XCS30XL);and miscellaneous support circuits (e.g., a 27C256 EPROM coupled to a4040 counter to provide clock signals, etc.). Analog components include:a crystal (e.g., 24 MHz) coupled to the microcontroller to provide amain system clock; voltage regulators (e.g., separate TPS76950 5-voltregulators for digital and analog components, a 78L033 3.3-voltregulator); decoupling capacitors; and RF circuitry for implementinggenerator 400, transmitter 500, and receiver 600.

For implementation of reference signal generator 400, RF circuitry ofexemplary device 300 suitably includes: an MMBF4416 FET and TK1235 RFtransformer, coupled together (gate to transformer via couplingcapacitor) along with associated RLC (resistor, inductor, capacitor)components for amplification of broadcasted signal 332; an NE602 mixerand associated RLC components; a 455 kHz ceramic filter; an LM7131op-amp with associated RLC components to serve as an IF amplifier; andan LM311 op-amp/comparator with associated components, including aresistor-capacitor “L-network” coupled to the LM311's inverting inputfor comparator hysteresis.

For implementation of receiver 500, RF circuitry of device 300 suitablyincludes circuitry similar to that implementing generator 400. TheTK1235 RF transformer is preferably replaced with a TK1237 version, andRLC component values suitably adjusted, to account for the differentfrequency of operation employed in receiver 500.

For implementation of transmitter 600, RF circuitry of device 300suitably includes: an MMBF4416 FET and TK1235 RF transformer, coupledtogether with associated RLC (resistor, inductor, capacitor) componentsfor amplification of an output signal to be transmitted; and a pair ofZC2811E diodes separated by an LM7131 op-amp stage (inverting, with DCbias of 2.5 volts) and selectably biased for on/off control of thetransmitter output signal.

Device 300 (FIG. 3) further includes a control module 310 coupled toreference signal generator 400, receiver 600, and transmitter 500 via anumber of data lines, represented as a group in FIG. 3 by a bus 320.Some of these data lines are illustrated in FIGS. 4–6. These include: amain system clock line 410; a transmit control line 510; a phaseintegrator output line 610; and a phase control line 520, which may beomitted if device 300 is used as a tracker in system 100. Data lines inbus 320 need not be physically grouped together or have any particularphysical form. In a variation where large portions of generator 400,receiver 600, and transmitter 500 are implemented by software in a DSP,particular “data lines” may be implemented by an intangible passing ofarguments from one software function to another.

Exemplary reference signal generator 400 produces two output signals ofsync pulses (unqualified and qualified types), which are represented asa group in FIGS. 3–6 by a bus 340. Generator 400 phase-stabilizes thesignals in bus 340 to broadcasted signal 332, which may be received fromany suitable broadcast source like transmitter 105 of FIGS. 1–2.Generator 400 receives signal 332 via a broadcasted signal line 330(FIGS. 3–4).

The internal operation of exemplary reference signal generator 400 maybe better understood with reference to FIG. 4. Generator 400 includes ananalog signal processing subsystem having an RF amplifier 420, a mixer422, a bandpass filter 424, and a comparator 426. Signal line 330couples broadcasted signal 332 to RF amplifier 420, which couples thesignal to mixer 422 with frequency selectivity (e.g., for imagerejection) and suitable amplitude. Mixer 422 frequency translates theselectively amplified signal to an IF (intermediate frequency), which is455 kHz in exemplary generator 400. Bandpass filter 424 rejects spuriousoutput signals from mixer 422 and defines selectivity of referencesignal generator 400 to one, and only one, broadcasted signal. (Invariations discussed below, a reference signal generator is maderesponsive to multiple broadcasted signals.) Comparator 426 acts as a1-bit A/D converter, providing a logic high signal on line 427 when theoutput signal from filter 424 exceeds a predetermined threshold andproviding a logic low signal on line 427 otherwise.

Reference signal generator 400 further includes a digital signalprocessing (DSP) subsystem 405. This subsystem is preferably implementedwithin a single FPGA with DSP subsystem 505 of transmitter 500 and DSPsubsystem 605 of receiver 600.

Signal line 427 enters DSP subsystem 405 and couples to a second mixer430 implemented in subsystem 405. Mixer 430 is controlled by the samelocal oscillator signal as mixer 422. Consequently, mixer 430 frequencytranslates the filtered, 1-bit signal on line 427 to the same frequencyas broadcasted signal 332 on line 330. The local oscillator signalcontrolling both mixers comes from local oscillator (LO) generator 432.

Generator 432 is a direct digital synthesis (DDS) module, commonlycalled a frequency synthesizer. In accordance with various aspects ofthe invention, such a module includes any functional module implementedby any suitable hardware, software, or combination of both that producesa periodic output signal by adding a predetermined increment to a phaseaccumulator. A DDS module typically achieves a periodic output bymodulo-adding the increment with a predetermined modulus. Generator 432produces a 1-bit output, which drives digital mixer 430 and, through anoutput port of the FPGA implementing DSP subsystem 405, analog mixer422.

Generator 432 is not phase-stabilized to any broadcasted signal, andconsequently its phase (and frequency) varies with variations in thefrequency of the clock (not shown) controlling DSP subsystem 405.Because mixers 422 and 430 perform complementary frequency translations,however, the output of first mixer 430 is phase-synchronous with theinput of second mixer 422.

The output of mixer 430, a 1-bit facsimile of the input to mixer 422,couples to a bandpass filter 434 for translation into a sinusoid thatthat very closely approximates a carrier of the selected broadcastedsignal 332 on line 330. In exemplary reference signal generator 400,filter 434 is an IIR bandpass filter having a single pole pair (i.e.,second-order) operating with 24-bit precision in its coefficients andoutput signal.

Generator 432 facilitates selection of a broadcasted signal for phasestabilization from a plurality of available broadcasted signals bymaking filter 434 digitally tunable. (Other techniques, many of themless convenient than that of generator 432, can be employed, e.g., localoscillator adjustment.) When device 300 is to operate in the SanFrancisco Bay area, for example, coefficients of filter 432 can bepredetermined such that filter 432 has a center frequency at 810 kHz,the operating frequency of radio station KGO. The coefficients areselected such that filter 434 has exceptionally high Q, e.g., abandwidth of about 60–80 Hz at the exemplary center frequency of 810kHz. Coefficients can be generated “on the fly” using conventionalfilter design equations. Alternatively, a lookup table can be providedcontaining coefficients for all available broadcasted signals, e.g., allof the approximately 100 AM broadcast channels available in the U.S.

Reference signal generator 400 requires no analog phase locking for itsoperation. Surprisingly, generator 400 can still phase stabilizetransmitter 500 and receiver 600 to a degree of stability greater thanthat which the 24 MHz clock of system 300 would conventionally permit.This advantageous phase stabilization is performed using a combinationof sync pulses (on signal line 450) and qualified sync pulses (on line460).

In exemplary generator 400, negative-to-positive transition detector 436derives sync pulses from zero crossing transitions of a highly filteredbroadcasted signal (output from filter 432). With any clocked digitalsystem, such transitions can only be determined to within a particularwindow of time uncertainty, which is proportional to the finite periodof the generator's system clock. For example, an observed zero crossingtransition may occur just before it is observed (upon transition of onesystem clock cycle), or it may occur nearly one full system clock cycleearlier, just after the previous system clock cycle has haltedobservation.

Qualified sync pulses are selected sync pulses that occur duringconditions meeting one or more predetermined criteria. Magnitudedetector 438 and “AND” gate 440 cooperatively produce qualified syncpulses when detector 436 has produced a corresponding sync pulse withina predetermined time before or after an actual zero crossing. In otherwords, qualified sync pulses are produced when the time uncertaintyinduced by clock granularity (e.g., 1/24 MHz clock period) randomlypermits a close match between the (unqualified) sync pulse and theactual event triggering it. This close match will typically occur whenthe trigger event occurs very shortly before or after transition of thegenerator's system clock.

Generator 400 employs zero crossing transitions as a trigger event. Thisconfiguration is advantageous in that it allows signal magnitude aroundthe zero crossing to be employed as a qualifying criterion for qualifiedsync pulses. Magnitude detector 438 determines whether the zero crossingtransition was observed close enough to the actual zero crossing thatthe signal level was less than or equal to a predetermined threshold(e.g., 1/64 its maximum value) at the observation time. If it was, thesync pulse (on line 450) resulting from the observation is consideredclose enough to being an accurate observation of its trigger event to beaccompanied by a qualified sync pulse, on line 460.

In variations, any predictable point along the cycle of a periodicsignal (to a resolution limited by system clock granularity) can beemployed as a trigger for a sync pulse and an associated qualifyingcriterion for a qualified sync pulse. For example, the point at which asignal reaches a predetermined threshold with a differential of a givensign (plus or minus) can be employed as a trigger. The differentialbetween the signal level and the threshold can be employed as aqualifying criterion.

Sync pulses on line 450 and qualified sync pulses on line 460 arerepresented together in FIGS. 3–6 by bus 340. Again, this is only anillustrative grouping; no particular physical bus structure is required.As discussed below, the sync pulse on line 450 and qualified sync pulseon line 460, in accordance with various aspects of the invention, form apowerful team of signals that facilitate completely digitalstabilization of phase well beyond the resolution of the system clockperiod.

Reference signal generator 400 couples sync pulses and qualified syncpulses to various DDS modules in transmitter 500 and receiver 600 forphase stabilization, via bus 340. In accordance with various aspects ofthe invention, these and other types of devices can be phase-stabilizedby including (1) a first DDS module whose phase accumulator is clockedby sync pulses, and a (2) second DDS module whose phase accumulator isclocked by system clock pulses but forced to the accumulated phase ofthe first DDS module when a qualified sync pulse occurs. The occurrenceof a qualified sync pulse indicates that the first DDS module was lastclocked by a sync pulse that was produced suitably close to apredetermined trigger event. That event is a predictable, consistentpoint along a periodic cycle of the broadcasted signal being employedfor phase stabilization.

When the serendipitously accurate clocking occurs, the output of thefirst DDS module accurately represents the phase that the second DDSmodule should have at that instant to achieve a desired phase stabilityand/or deviation. (As discussed below with reference to FIG. 6, apredetermined phase deviation can actually be induced in a DDS module toimpart overall phase stability.) As discussed below, a less accuratesystem clock, i.e., a clock operating further from its expectedfrequency, causes the accumulated phase of the second DDS module to befurther deviated from the accumulated phase of the first DDS module. Insuch cases, the second DDS module's accumulated phase undergoes moresignificant correction when qualified sync pulses occur.

An example of phase stabilization according to various aspects of theinvention may be better understood with reference to the simulatedsignal plots of FIGS. 10–15. A computer program listing below providescode that was executed with the Octave numerical language environment(similar to MATLAB) to produce these plots.

FIGS. 10 and 11 illustrate multiple signals produced during thesimulation with (1) a fairly accurate system clock frequency, and (2) aless accurate clock frequency. The signals depicted are: a system clockhaving segments 1010 (FIG. 10) and 1110 (FIG. 11); a broadcasted signalwith segments 1020, 1120 on which phase stabilization is based;sequences 1030, 1130 of regular (unqualified) sync pulses; sequences1040, 1140 of qualified sync pulses; a sinusoid-transformed rendition ofa phase stabilization signal having segments 1050, 1150; an unstabilizedoutput signal with segments 1060, 1160 (illustrated for comparison); anda stabilized output signal having segments 1070, 1170.

In the simulation, the nominal clock frequency is modeled at 24 MHz. Thefrequency of the broadcasted signal (segments 1020 and 1120 of FIGS. 10and 11) is modeled at 5 MHz, and the desired frequency of the outputsignal is modeled at 3.5 MHz. The 24 MHz clock frequency is sometimesemployed in FPGA devices currently available, and 5 MHz is one of thefrequencies of NIST broadcast transmitter WWV. However, these are onlyexemplary signals and frequency values, which do not in any way limitthe possible signals employed during implementation of the invention.

The simulation generated 4096 data points for each signal, with eachpoint representing approximately 1/20 of a system clock cycle at itsexpected frequency of 24 MHz. The points are too close together to beindividually identifiable in the plots of FIGS. 10–15, but they providea convenient reference frame on the X-axis (i.e., the time axis) of theplots of FIGS. 10–13.

FIG. 10 depicts the simulated signals in the interval from points 0001through 1024. During this interval, five qualified sync pulses occur, insequence 1040. The simulation generated these qualified sync pulses whenit had generated a corresponding sync pulse in sequence 1030sufficiently close to a zero crossing of the broadcasted signal insegment 1020. The simulation qualified this closeness to the zerocrossing using the criterion that the broadcasted signal have anamplitude less than 15% of its maximum. (For clarity of illustration,this simulation criterion was set much higher than the 1/64=1.5%criterion of reference signal generator 400 of FIG. 4.) This portion ofthe simulation, and the method it exemplifies, may be better understoodwith reference to lines 52–65 of the program listing below.

During its segment 1010 within this interval, the system clock wasfairly close to its expected frequency. See lines 10, 26, and 30–31 ofthe program listing for a better understanding of how the simulationmodeled a time-varying deviation in system clock frequency.

In their respective segments 1060 and 1070 within the 0001–1024 pointinterval of FIG. 10, the unstabilized output signal and the stabilizedoutput signal look very similar. This similarity exists because theaccumulated phase of the stabilized DDS module (simulated at lines100–115 of the program listing) did not undergo a very dramaticcorrection when qualified sync pulses of sequence 1040 occurred, e.g.,at time T₁.

At time T₁, system clock transition 1012 caused the simulated system toobserve a zero crossing transition 1022 and generate a sync pulse 1032shortly after the transition actually occurred. (To keep the plotscompact, both positive and negative clock transitions were recognized.)The observation was accurate enough that the broadcasted signal insegment 1020 was unable to reach 15% of its maximum amplitude by thetime the observation was made. Consequently, the simulated systemgenerated a qualified sync pulse 1042 in sequence 1040.

Qualified sync pulse 1042 forced the phase accumulator of the stabilizedDDS module to the accumulated phase of a stabilizing DDS module, whichwas simulated at lines 76–85 of the program listing. Portion 1052 of theDDS module's phase stabilization signal is at the accumulated phase(transformed to a sinusoid in FIG. 10) to which qualified sync pulse1042 forced the stabilized DDS module. This forcing caused thestabilized output signal in segment 1070 to reach a very slightlydifferent amplitude at portion 1072, upon transition of the systemclock, from what it would have without forcing. Because the system clockin segment 1010 is close to its expected frequency, the forcing is notvisually apparent in segment 1070 of the stabilized output signal.

In the interval from about points 3084 through 4096, depicted in FIG.11, the effect of phase stabilization according to various aspects ofthe invention is much more apparent. During its segment 1110 within thisinterval, the system clock was significantly deviated from its expectedfrequency. A visual comparison shows that the clock frequency in segment1110 was significantly higher than in segment 1010.

The broadcasted signal had the same frequency in both segment 1120 andsegment 1130, which is consistent with the broadcasted signal being froma source that is phase stable. Although the invention does not require abroadcasted signal to have any minimum phase stability, it does not makemuch sense in typical implementations to phase stabilize an output to ahighly unstable signal.

At time T₂, as at time T₁ of FIG. 10, the occurrence of a qualified syncpulse 1142 forces the output DDS module's phase accumulator to the valueof the phase stabilization signal in sinusoid-transformed segment 1150,at portion 1152. Here, this forcing causes the stabilized output signalin segment 1170 to make a dramatic transition at portion 1172. Thistransition results in a significant phase change, visibly stretching thenegative half-cycle of the stabilized output signal.

FIGS. 12 and 13 are time-domain plots of the unstabilized and stabilizedoutput signals, respectively, after they passed through a filter havinga narrow passband at the expected output frequency. (See lines 135–155of the program listing.) These plots, which span the entire 4096simulation points, illustrate how the frequency of the unstabilizedoutput signal varied with system clock frequency and how the frequencyof the stabilized signal resisted such variation.

At the beginning of the simulation, points 500–1000 (all references tosimulation data points are approximate), the filtered outputs graduallyrose to maximum amplitude, a phenomenon resulting from the filterimpulse response rather than the output signal themselves. Betweenpoints 500–1000, the system clock remained within about 4% of itsexpected frequency (program listing, line 26), and both signals remainedsubstantially within the narrow passband of the simulation's bandpassfilter.

Between points 1000–2000, the system clock rose from about 4% greaterthan its expected value to a positive deviation of about 9%. In thisinterval, the difference in frequency between the unstabilized andstabilized output signals is visually noticeable in FIGS. 12 and 13. Theunstabilized output signal (FIG. 12) steadily decreased in amplitude asits frequency drifted outside the filter passband. The stabilized signal(FIG. 13) remained within a 3 dB amplitude range as its primaryfrequency component remained substantially within the filter passband.

As the clock frequency continued to increase beyond point 2000, towardits maximum positive deviation of 25%, the unstabilized signal of FIG.12 continued to drift further away from the simulation filter passband.The stabilized signal of FIG. 13 increased and decreased in amplitude,though a 3.5 MHz frequency component clearly remained within thepassband of the simulation filter at various times. The simulationexemplifies that, even with the 10–25% deviation from an expected clockfrequency, with the dramatic phase corrections illustrated in FIG. 11,phase stabilization according to various aspects of the invention canstill operate under certain circumstances. In typical implementations,however, clock frequency deviations are likely to be measured in theparts per million, and maintaining consistent performance with suchdramatic clock frequency deviations is then unnecessary.

Perhaps the clearest depiction of performance in the simulation of phasestabilization according to various aspects of the invention is found inthe X-Y plots FIGS. 14 and 15. FIG. 14 depicts phase differences betweentwo intervals of the unstabilized filter output signal, with theamplitude of points 500–900 plotted on the X-axis and the amplitude ofpoints 1500–1900 plotted on the Y-axis. Phase increases of the signal inone region clearly outpaced those of the signal in the other region, anda frequency difference between the signal in the two regions is thusclearly apparent.

FIG. 15 depicts the same types of phase differences in the same regions(points 500–900 vs. points 1500–1900), but for the stabilized filteroutput signal. The clean ellipse of FIG. 15 is a clear illustration ofthe advantageous result of phase stabilization performed according tovarious aspects of the invention. With this simulated phasestabilization, the stabilized output signal maintained a relativelyconstant phase (and frequency) relationship even with clock frequenciesvarying between about 2% (simulation point 500) and about 8% positivedeviation.

Exemplary device 300 of FIG. 3 includes a transmitter 500 and receiver600 that are phase-stabilized in accordance with the various aspects ofthe invention discussed above. Functional modules of transmitter 500 areimplemented mostly in a DSP subsystem 505. As illustrated in FIG. 5,exemplary transmitter 500 includes just one analog signal processingcomponent: a selectable output amplifier 590. Control module 310 canenable or disable operation of amplifier 590 via transmit control line510, which is part of bus 320 of FIG. 3.

DSP subsystem 505 includes a transmit DDS module 530, which isphase-stabilized to broadcasted signal 332 by a stabilizing DDS module532. DDS modules 530 and 532 act cooperatively under control of syncpulses and qualified sync pulses from bus 340 to produce a transmitsignal 595 that is phase-stabilized to broadcasted signal 332. TransmitDDS module 530 includes a phase accumulator (none are shown) thatproduces transmit signal 595 by having its value increased by apredetermined increment with each system clock cycle. The increment isset to the transmit frequency divided by the nominal system clockfrequency.

Stabilizing DDS module 532 includes a phase accumulator that produces aphase stabilization signal by having its value increased by apredetermined increment with each sync pulse on line 450. The incrementfor stabilizing DDS module 532 is set to the transmit frequency dividedby the broadcasted signal frequency. The increment is computed with asuitable modulus for phase increments beyond 360 degrees per sync pulse,i.e., when several transmit signal cycles are expected between eachcycle of the broadcasted signal.

Qualified sync pulses appearing on line 460 force the phase accumulatorof transmit DDS module 530 to the value of the phase stabilizationsignal from module 532. A similar process in another example isdescribed above with reference to simulated signal plots of FIGS. 10–15.The phase-stabilized transmit signal is suitably amplified by amplifier590 (when it is enabled by transmit control line 510) and the signal 595is transmitted via a suitable coupling device, e.g., a whip or loopantenna, a piezoelectric transducer, etc.

Exemplary receiver 600 of FIG. 6 receives a signal at line 602 via asuitable coupling device, preferably the same device from which thetransmitter 500 of FIG. 5 transmits signal 595. Receiver 600 includes ananalog signal processing subsystem having a bandpass filter 618, an RFamplifier 620, a mixer 622, a bandpass filter 624, and a comparator 626.Signal line 602 couples the received signal to bandpass filter 618,which performs image rejection and protects RF amplifier 620 and mixer622 from high-amplitude extraneous signals. Bandpass filter 618 couplesthe filter signal to RF amplifier 620, which amplifies it and overcomesthe noise figure of mixer 622. Mixer 622 frequency translates thefiltered and amplified signal to an IF (intermediate frequency), whichis 455 kHz in exemplary receiver 600. Bandpass filter 624 rejectsspurious output signals from mixer 622 and largely defines selectivityof receiver 600. Comparator 626 acts as a 1-bit A/D converter, providinga logic high signal on line 627 when the output signal from filter 624exceeds a predetermined threshold and providing a logic low signal online 627 otherwise.

The digital signal on line 627 enters a DSP subsystem 605 of receiver600 and couples to a second mixer 630 implemented in subsystem 605.Mixer 430 frequency translates the filtered, 1-bit signal on line 627 toa baseband signal, which is integrated by a summing module 640.

The local oscillator signal (a 1-bit signal from an FPGA output line)controlling analog mixer 622 comes from a first local oscillator DDSmodule 650, which is unstabilized. The local oscillator signalcontrolling digital mixer 630 comes from a second local oscillator DDSmodule 660, which is phase-controlled by a stability compensating DDSmodule 662.

DDS modules 660 and 662 cooperatively form a phase-stabilizing signalgenerator. A phase-stabilizing signal generator according to variousaspects of the invention includes any hardware, software, or combinationof both producing an output with phase that varies in a useful,predictable manner with respect to a reference signal, e.g., abroadcasted signal. Such variation can be configured to be opposite theexpected variation of an unstabilized signal generator. In receiver 600,the outputs of the phase-stabilizing generator formed by DDS modules 662and 660 and unstabilized signal generator 650 are applied to successivemixers 622 and 630.

Stability compensating DDS module 662 causes mixer 630 to frequencytranslate the first IF signal at line 627 with an induced phaseinstability. This phase instability is opposite that of stabilized DDSmodule 650, and opposite the phase instability that mixer 622consequently imparts to the received signal. Advantageously, the phaseinstabilities cancel each other out. The signal integrated by summingmodule 640 (e.g., for four seconds or about 100×10⁶ samples clocked at24 MHz) is substantially phase stable with respect to sync pulses on bus340, and with respect to the broadcasted signal on line 330 thatgenerates them.

The output of summing module 640, on line 610, varies with the phase ofthe received signal. Line 610 couples via bus 320 to control module 310,where device 300 can implement functions of a spatial position computer.When device 300 is employed as tracker 110 of system 100, for example,the spatial position computer it implements determines a spatialposition of transmitter 114 and receiver 116 (which is typically but notnecessarily the same as the position of tracker 110 itself) relative totransponder 150.

As mentioned above, the configuration discussed with reference to FIGS.3–6 is merely exemplary. Again, a tracker, transponder, reference signalgenerator, transmitter, and receiver according to various aspects of theinvention can include any suitable hardware, software, or combination ofboth for performing the respective functions of those devices.

Spatial position determination according to various aspects of theinvention may be better understood with reference to an exemplary method700 of FIG. 7. Method 700 begins at process 710, at which the trackertransmits a forward signal having phase φ_(A). This phase represents theunknown, non-referenced phase of a transmitted signal after passingthrough various stages of signal processing. Method 700 continues atprocess 720, at which a transponder receives the signal with a phase α.As shown in FIG. 7, phase α is directly proportional to the distancebetween tracker and transponder. Phase α also includes an unknownadditive term θ_(A) that results from signal processing phase shifts inthe transponder receiver.

At process 730, the transponder transmits a return signal at thereceived phase α. The return signal, as transmitted at the transponder,is thus also directly proportional to the distance between tracker andtransponder. When received at the tracker, at process 740, the returnsignal phase φ_(B) is directly proportional to twice this distance.Phase φ_(B) also includes an unknown additive term θ_(B) that resultsfrom signal processing phase shifts in the tracker receiver.

Method 700 concludes at process 750, at which a spatial positioncomputer (preferably in the tracker device itself) determines distance(including some unknown additive term) based on stored indicia ofwavelength(s), here a common wavelength λ, of the forward and returnsignals.

A method 800 for determining an offset from a previous spatial position(here, change in distance) may be better understood with reference toFIG. 8. In addition, a method 900 for determining spatial positionexpressed as an azimuthal angle may be better understood with referenceto FIG. 9.

Method 800 involves movement to three locations, by processes 810, 820,and 830. At these locations, three distance measurements d₁, d₂, and d₃are obtained, by processes 812, 822, and 832, respectively. The additiveterms θ_(A) and θ_(B) prevent determination of an absolute spatialposition (here, distance) based on a single measurement. Thus, themeasured distance values d₁, d₂, and d₃ are proportional values that allinclude some unknown additive term.

Process 840 determines an offset Δd₁ from d₂ and the previous spatialposition d₁. Similarly, process 850 determines an offset Δd₂ from d₃ andthe then-previous spatial position d₂. These offsets (i.e., changes indistance) are output to a user by process 860. Though FIG. 8 depictsthree distance measurements, this is only exemplary. As few as two cangive meaningful results, and many more measurements are likely to bemade during a typical search using a system according to various aspectsof the invention.

Method 900 of FIG. 9 also involves movement to three locations, byprocesses 910, 920, and 930. Unlike method 800, method 900 includesprocesses 914, 924, and 934 for determining tracker position at thesethree locations, expressed as relative X and Y coordinates (X₁,Y₁),(X₂,Y₂), and (X₃,Y₃). The locations can be determined based oninstructions to a user. For example, a user may be instructed to “take ameasurement, move three paces north, take a measurement, then move threepaces east and take a measurement.” In an advantageous variation,processes 914, 924, and 934 can employ a position determination device(e.g., optional GPS module 122 of tracker 110) to determine positionalcoordinates for multiple locations as the user moves about in search ofa lost object.

Processes 912, 922, and 932 obtain three distance measurements d₁, d₂,and d₃ at the respective known locations. Preferably, these processes,and processes 812, 822, and 832 of method 800, each perform an instanceof method 700 of FIG. 7. Based on the known coordinates (X₁,Y₁),(X₂,Y₂), and (X₃,Y₃) and associated distance measurements d₁, d₂, andd₃, process 940 determines spatial position, which can be expressed anddisplayed as an azimuthal angle from tracker to transponder.

Process 940 can employ any suitable technique for such positiondetermination. For example, the azimuthal angle can be computed from theequation φ=tan⁻¹ (Δd₁/Δd₂). Given enough measurements, process 940 mayalso compute a rough near/far approximation of absolute distance betweentracker and target.

Public Notice Regarding the Scope of the Invention and Claims

The inventor considers various elements of the aspects and methodsrecited in the claims filed with the application as advantageous,perhaps even critical to certain implementations of his invention.However, the inventor regards no particular element as being“essential,” except as set forth expressly in any particular claim. Thefollowing are various systems, devices, and methods contemplated by theinventor that omit various advantageous but non-essential elementsdiscussed above.

A spatial position determination system, which omits transponder 150 ofFIG. 2, includes a tracker reference signal generator that is coupled toand phase-stabilized by a broadcasted signal. The system furtherincludes a tracker transmitter and tracker receiver that are bothcoupled to and phase-stabilized by the tracker reference signalgenerator. The system further includes a spatial position computer thatis coupled to the tracker receiver and at least one of the trackerreference signal generator and the tracker transmitter. The spatialposition computer is responsive to indicia of a phase relationshipbetween an output signal from the tracker transmitter and an inputsignal to the tracker receiver. Thus, the spatial position computer candetermine a spatial position of the tracker transmitter and trackerreceiver relative to a source of the input signal to the receiver.

An active reflector contemplated by the inventor, which omits tracker110 of FIG. 2, includes a receiver and a transmitter that isphase-controlled by the receiver. Such a device advantageously transmitsa signal having a phase determined by the phase of the signal receives.Consequently, the device provides an “echo” of a signal for phase-baseddistance measurement without the need to overcome path loss for both theforward and return trip, as well as passive reflection loss and phaseuncertainty induced by an irregular reflecting surface.

A phase-stabilized or phase-stabilizing signal generator, which can beadvantageously employed in any device requiring an outputphase-stabilized to an input, includes (1) a first DDS module having aphase accumulator that is clocked responsive to sync pulses, and (2) asecond DDS module, coupled to the stabilizing frequency synthesizer andhaving a phase accumulator that is clocked by system clock pulses butforced to the accumulated phase of the first DDS module upon occurrenceof a qualified sync pulse.

A phase-stabilized signal generator produces an output of substantiallythe same phase stability as the source of sync pulses and qualified syncpulses. A phase-stabilizing signal generator produces an output withphase that varies in a useful, predictable manner with respect to thesource of pulses. As discussed above, such variation can be configuredto be opposite the expected variation of an unstabilized signalgenerator. When the outputs of the phase-stabilizing and unstabilizedsignal generators are applied to successive mixers in a signalprocessing chain, the opposite variations cancel each other out. Asignal that is frequency translated by the signal processing chain canthus avoid phase instability from the unstabilized signal generator.

While the invention is described herein in terms of preferredembodiments and generally associated methods, the inventor contemplatesthat alterations and permutations of the preferred embodiments andmethods will become apparent to those skilled in the art upon a readingof the specification and a study of the drawings. Below is a listing ofsome examples of variations contemplated by the inventor and fallingwithin the scope of the claims unless excluded by specific claimlanguage.

EXAMPLE A

Instead of transmitting an unmodulated carrier as described above,tracker 110 can transmit a carrier phase modulated by a pseudo-randomsequence. The chip time (i.e., duration of each phase modulation symbol)can be determined by the time base shared by the tracker and the target.The chip rate can be a predetermined fraction of the carrier frequency,or a predetermined fraction of the broadcasted signal's frequency.

Transponder 150 performs a correlation maximization search to determinethe start time of the pseudo-random sequence. This correlation needs tobe performed only during the initial synchronization acquisitionprocess. All subsequent transmissions can remain synchronized due to thecommon time base.

In this variation, system 100 relies on the ability of both tracker 110and transponder 150 to measure the phase of the signals they eachreceive. The DSSS phase modulation does not interfere with thismeasurement. In each DSSS receiver the incoming signal is multiplied bythe pseudo-random phase sequence to yield a constant phase receivedsignal.

The phase-modulated DSSS signal has a spectral bandwidth proportional tothe chip rate. An equalization filter can be applied to reduce theeffect of variable group delay across the band. This filter does notnecessarily interfere with the phase measurement of the incoming signal.For example, without loss of generality, the equalization filter can bechosen to have zero phase at the carrier frequency.

EXAMPLE B

In some implementations, it may be desirable to phase stabilize to an FMbroadcast station. However, FM signals do not have constant phase.Variations of tracker 110 and transponder 150 may overcome this issue byboth computing an averaged reference signal in the same way. Forexample, each unit may compute the instantaneous broadcast frequency tobe 10⁷ divided by the time elapsed during the previous 10⁷ cycles.Continuous computation would require a circular buffer.

EXAMPLE C

Phase stabilization can be to subcarriers of a broadcasted signal ratherthan carrier of the signal. For example, variations of reference signalgenerators 112 and 152 can phase stabilize other components to thecolor-burst frequency from TV stations, or to commercial subcarriersfrom FM broadcast stations.

EXAMPLE D

Frequency synthesis can be performed in the optical domain. Nonlinearoptical media can be used to generate a transmitted signal or signalsfrom a broadcasted coherent light signal. For example, if lightgenerated by a single laser is dispersed over an area including atracker and transponder, nonlinear optical media in each unit can beemployed to generate the same phase-coherent type of light, of awavelength different from that of the dispersed laser light.

EXAMPLE E

In typical implementations, the broadcasted signal is received by both atracker and transponder from an external transmitter. With a suitablystable self-contained oscillator in either unit, however, such a signalcan be broadcasted from that unit, received by the other, and employedby both for phase stabilization.

EXAMPLE F

Systems not requiring the benefits of digital phase stabilization canemploy one or more conventional phase-locked loops (e.g., with a VCXO)for phase stabilization.

EXAMPLE G

An advantageous use of system 100 is the location of buried avalanchevictims and missing skiers, hikers, firefighters, etc. Many ski resortshave poor broadcasted signal reception due to remoteness and surroundingmountains. To overcome this issue, a variation of broadcast transmitter105 can be a local broadcast beacon having transmission coverage over anarea that includes potential avalanche sites.

EXAMPLE H

In a variation, the transponder can transform the received forwardsignal with a nonlinear transfer function. The frequency scaled signalin such a variation is a harmonic of the received forward signal. Asdefined herein and in Barry Truax, ed., Handbook For Acoustic Ecology(1999), a harmonic is an integer multiple of a fundamental and asubharmonic is an integer submultiple or fraction of a fundamental.

EXAMPLE I

In another variation, the transponder can digitally frequency divide thereceived forward signal, whereby the frequency scaled signal is asubharmonic of the received forward signal.

EXAMPLE J

In another variation, the transponder can digitally synthesize thefrequency scaled signal responsive to the received forward signal,whereby the frequency scaled signal is a subharmonic of the receivedforward signal.

EXAMPLE K

A loop antenna could be substituted for the whip antenna 112 of FIG. 1.

EXAMPLE L

The antenna for transponder 150 can be a ferrite loopstick, or anysuitable alternative. One such alternative is including a conductiveloop in the collar of dog 155 that carries transponder 150. Preferably,the loop is resonated with suitable capacitive tuning of the loop, withoptional resistive Q dampening and an at least partially horizontal looporientation (as illustrated in FIG. 1) to avoid directional nulls.

EXAMPLE M

Phase-stabilizing tracker 110 and transponder 150 to a single AMbroadcast station (one of many options) requires both devices to choosethe same station. In a variation, each unit can phase stabilize tonumerous receivable AM stations in an aggregate, weighting eachstation's influence by the receive strength for that station to yield areference signal whose phase varies slowly with the geographicalposition of the unit.

Accordingly, neither the above description of preferred exemplaryembodiments, nor the code listing of a merely illustrative simulatedembodiment below, nor the abstract defines or constrains the invention.Rather, the issued claims variously define the invention. Each variationof the invention is limited only by the recited limitations of itsrespective claim, and equivalents thereof, without limitation by otherterms not present in the claim. For example, claims that do not reciteany specific components of a spatial position computer read on methodsthat include, and exclude, advantageous components recited in otherclaims, such as memory cells including indicia of a plurality ofprevious spatial positions. As another example, claims not recitinglimitations regarding components of a transponder read on devices andmethods that include, and exclude, advantageous components such as atransponder reference signal generator.

In addition, aspects of the invention are particularly pointed out inthe claims using terminology that the inventor regards as having itsbroadest reasonable interpretation; the more specific interpretations of35 U.S.C. § 112(6) are only intended in those instances where the terms“means” or “steps” are actually recited. The words “comprising,”“including,” and “having” are intended as open-ended terminology, withthe same meaning as if the phrase “at least” were appended after eachinstance thereof.

COMPUTER PROGRAM LISTING 1 %%% SPATIAL POSITION DETERMINATION SYSTEM 2%%% Timing Analysis 3 %%% Runs on Octave, a GPL alternative to MATLAB 4% 5 N = 4096; % No. of pts. 6 i = 1:N; % pts. in vectors 7 C = 3; %Scaling of displayed sync pulses 8 qt = 0.15; % Threshold for qualifiedsync pulses 9 % Frequency error (fraction of clock freq. at each end) 10fe = 0.25; 11 % 12 %%% Define frequencies 13 fclk = 24E6; 14 ftx =3.5E6; 15 fbs = 5E6; 16 % 17 %%% Define max time and time vector 18 T =200*(1/fclk); 19 t = (i/N)*T; 20 % 21 %%% Define base signal vectors 22%%% Assign plot offset to each displayed signal 23 % 24 % Frequencyerror in clock (should be visible) 25 ferr = linspace(0,1,N); 26 ferr =fe/2*fclk*( ferr.{circumflex over ( )} 2 ) + fe/2*fclk*ferr; 27 % 28 %System Clock 29 prand = rand; % Random phase component 30 f =fclk*ones(1,N) + ferr; 31 sclk = exp( j*2*pi*( f .* t + prand) ); 32clk_scale = 2.5; 33 sclk = clk_scale*sign(real(sclk)) .* . . . 34 min(1/clk_scale*ones(1,N) , abs(real(sclk)) ); 35 oclk = 15; 36 % 37 %Broadcasted signal 38 sbs = exp(j*2*pi*fbs*t); 39 obs = 12; 40 % 41 %sync pulses 42 kk = 1; 43 SBS = [1 0]; 44 for k = 2:N 45 if (sign(real(sclk(k))) ~= sign(real(sclk(k−1))) ) 46 SBS(kk,2) = sbs(k); 47SBS(kk,1) = k; 48 kk = kk+1; 49 end % endif 50 end % endfor 51 % 52 sync= zeros(1,N); qsync = zeros(1,N); 53 SYNC = [ ]; QSYNC = [ ]; 54 for k =2:max(size(SBS)) 55 if ( sign(real(SBS(k,2))) ~= sign(real(SBS(k−1,2)))) 56 sync( SBS(k,1) ) = 1; 57 SYNC = [ SYNC SBS(k,1) ]; 58 if (abs(real(SBS(k,2))) < qt ) 59 qsync( SBS(k,1) ) = 1; 60 QSYNC = [ QSYNCSBS(k,1) ]; 61 end % endif 62 % 63 end % endif 64 end % endfor 65 sync =sync(1:N); % Trim if necc. 66 osync = 9; 67 oqsync = 7; 68 % 69 %Synthesize phase-stabilizing signal 70 pinit = 0; 71 % 72 % SIMULATION73 kk = 1; 74 while (kk > 0) 75 % 76 % Stabilizing Synthesizer 77 pstab= [ ]; 78 pa1 = ftx / fbs; % Phase increment 79 p1 = pinit; % Initialphase 80 for k = 1:max(size(SYNC))−1 81 p1 = rem(p1+pa1,1); 82 pstab(SYNC(k):SYNC(k+1)−1 ) = p1; 83 end % endfor 84 pstab( SYNC(k+1):N ) =rem(p1+pa1,1); 85 sstab = exp(j*2*pi*pstab); % Convert phase to sinusoid86 ostab = 5; 87 % 88 % TX Synthesizer (unstabilized) 89 ptxu = [ ]; 90pa2 = ftx / fclk; % Phase increment 91 p2 = 0; % Initial phase 92 for k= 2:max(size(SBS)) 93 p2 = rem(p2+pa2,1); 94 ptxu( SBS(k−1,1):SBS(k,1) )= p2; 95 end % endfor 96 ptxu( SBS(k,1):N ) = rem(p2+pa2,1); 97 stxu =exp(j*2*pi*ptxu); % Convert phase to sinusoid 98 otxu = 2; 99 % 100 % TXSynthesizer (stabilized) 101 ptx = [ ]; 102 pa3 = ftx / fclk; % Phaseincrement 103 p3 = 0; % Initial phase 104 for k = 2:N 105 % 1 if match,0 if none 106 match = length( find( QSYNC==k ) ); 107 if ( match ) 108p3 = pstab(k); % Force to “correct” phase 109 elseif (sign(real(sclk(k))) ~= sign(real(sclk(k−1))) ) 110 % Not a qual. syncpulse, so don't force 111 p3 = rem(p3+pa3,1); 112 end % endif 113 ptx(k)= p3; 114 end % endfor 115 stx = exp(j*2*pi*ptx); % Convert phase tosinusoid 116 otx = −1; 117 % 118 kk = input(‘Enter frame # 1,2,3, or 4(0 to quit): ’); 119 % 120 k1 = max(1,(N/4)*(kk−1)+1); k2 =min((N/4)*kk,N); 121 % 122 pst = “r”; 123 subplot(1,1,1); plot([0 1]);pause; 124 plot( . . . 125 i(k1:k2),real(sbs(k1:k2))+obs,pst, . . . 126i(k1:k2),real(sclk(k1:k2))+oclk,pst, . . . 127i(k1:k2),sync(k1:k2)+osync,pst, . . . 128i(k1:k2),qsync(k1:k2)+oqsync,pst, . . . 129i(k1:k2),sstab(k1:k2)+ostab,pst, . . . 130i(k1:k2),stxu(k1:k2)+otxu,pst, . . . 131 i(k1:k2),stx(k1:k2)+otx,pst);132 % 133 end % endwhile 134 % 135 %%% Display filtered signals 136 %137 fc = 2*ftx; % Set fc to “correct” frequency of ftx 138 Nc = ceil(fc*T ); % No. of Fourier steps in passband 139 % 140 % Build passbandvector 141 F = zeros(1,N); 142 F(Nc−2:Nc+2) = [1 1 1 1 1]; 143 % Filtercoeffs. 144 b = real(ifft(F)); 145 Nb = 512; 146 b = Nb*hamming(Nb+1)'.*fftshift([b(2:Nb/2) b(1) b(N−Nb/2:N)] ); 147 % 148 subplot(1,1,1);plot([0 1]); pause; 149 % 150 stxu_f = filter(b,1,stxu); 151 stx_f =filter(b,1,stx); 152 Nf = length(stxu_f); 153 % 154 subplot(2,1,1);plot(1:Nf,real(stxu_f),pst); 155 subplot(2,1,2);plot(1:Nf,real(stx_f),pst);

1. A spatial position determination system comprising: (a) a trackerunit comprising: (1) a reference signal generator responsive to andphase-stabilized by a broadcast signal; (2) a transmitter coupled to andphase-stabilized by the reference signal generator; and (3) a receivercoupled to and phase-stabilized by the reference signal generator andresponsive to a return signal from a transponder unit that is coupledvia field radiation to the tracker unit, which return signal istriggered by a signal from the transmitter; and (b) a spatial positioncomputer coupled to the receiver and at least one of the referencesignal generator and the transmitter, responsive to indicia of a phaserelationship between an output signal from the transmitter and thereturn signal; whereby the spatial position computer determines aspatial position of the tracker unit relative to the transponder.
 2. Thesystem of claim 1 wherein the reference signal generator is responsiveto a commercial broadcast signal.
 3. The system of claim 2 wherein thereference signal generator is responsive to a commercial broadcastsignal in a frequency range between about 500 kHz and about 1600 kHz. 4.The system of claim 1 wherein, during operation: (a) the spatialposition computer includes a memory cell that includes indicia of aprevious spatial position; and (b) responsive to the indicia, thespatial position computer determines the spatial position of the trackerunit relative to a source of the return signal, the spatial positionbeing expressed as an offset from the previous spatial position.
 5. Thesystem of claim 1 wherein, during operation: (a) the spatial positioncomputer includes a memory cell that includes indicia of wavelength ofat least the return signal; and (b) responsive to the indicia, thespatial position computer determines the spatial position of the trackerunit relative to a source of the return signal, the spatial positionbeing expressed as a physical measure of distance.
 6. The system ofclaim 1 wherein, during operation: (a) the spatial position computerincludes memory cells that include indicia of a plurality of previousspatial positions; and (b) responsive to the indicia, the spatialposition computer determines the spatial position of the tracker unitrelative to a source of the return signal, the spatial position beingexpressed as an azimuthal angle from the tracker unit.
 7. The system ofclaim 1 further comprising a controller coupled to the transmitter andconfigured to periodically enable and disable signal transmissiontherefrom.
 8. The system of claim 1 further comprising a digital signalprocessing subsystem that, during operation, implements at leastportions of the reference signal generator, transmitter, and receiver ofthe tracker unit.
 9. The system of claim 8 further comprising a controlsubsystem that, during operation, implements at least portions of thespatial position computer.